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The Nursing Workforce - 2010Appendix 2. Specification of the dynamic modelRegistered nursesWe adopt index t to denote year, and k to denote k th age group of nurses. The variables are defined as following:
The aggregate number of nurses, new nurse graduates, net exit, nurse intake and migrant nurses are: The model is simply based on an identity: the annual increase of the number of nurses in the workforce (in year t and age group k ) must be equal to the net inflow of nurses (intake minus exit) into the workforce in the same year and the same age group10: The first term on the right hand side of (A2.2) is due to ageing: the nurses of the previous year (t-1) in the younger age group (k-1) move to the age group k this year (t). The second term of (A2.2) in the bracket is the net influx of nurses in year t and age group k. New nurses supplies can be expressed by The value of each
Our dynamic nurse model can first be used to obtain the historical net nurse exit rates. Using (A2.3) and rewriting (A2.2), we arrive at the nurse net exits: The net nurse exit rates are then11 A proper modelling of (A2.5) requires Once the net exit rate The aggregate exit rates, derived from (A2.4) and (A2.5a), are Enrolled nursesThe limitation of the enrolled nurse graduate data prohibits us from adopting an identical approach as used previously for enrolled nurses. However, we can apply the same method at the aggregate level. The (net) aggregated exit rates each year can be obtained from (A2.4): In (A2.7), we have assumed that there is no delay between course completion
and being a nurse. This treatment makes the calculation easier. As we shall see
in the appendix 3 that a mean exit rate over six years is adopted, this
assumption does not affect much the projection for the enrolled nurses. Having
obtained the exit rate This is a linear projection given a constant aggregate exit rate, new graduate and migrant nurses. However, it can be argued that the workforce of enrolled nurses will age in a similar way to the workforce of registered nurses because of the resemblance of their initial age distributions. We can add the percentage point change of the aggregate exit rate derived from the registered nurse on to that of the enrolled nurses. Figure A2.1 projected aggregate exit rates for registered and enrolled nurses (2000-2020). This method is used in Table 4.3 to derive future aggregate exit rates for the enrolled nurses. Figure A2.1 Projected aggregate exit rates for registered and enrolled nurses, 2000-2020
Foot Notes: 10.The continuous form of this difference equation is , with k here as a continuous variable to describe the date of birth. In discretising this equation with a time unit one year, O needs to be the final count of the number of nurses at the end of the year. 11.Note that we define the exit rate with lag in time and age group but this definition may be arbitrary. 12.In this case, an extrapolation of G before 1995 is still necessary, though this approximation is not crucial.
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